A B737-400 encountered a flap asymmetry situation and diverted to an airport with a longer runway. Flaps retracted normally after landing.

Narrative

I was the Flying Pilot and had configured to flaps 10; holding 180 kts until just before the bridge; and then asked for gear down; flaps 15 and the landing checklist. Since my ref speed was 133 knots; I bugged the speed back to 138 kts. At approximately 150 kts I called for flaps 30 and then shortly after called for flaps 40. It quickly became apparent the aircraft was not slowing as I expected and then my First Officer called; 'Flap Asymmetry.' The left flap was at approx 16 and the right flap was at approx 12. I was now approaching 1000 AGL and decided that we would need to go around and give ourselves more time to sort out our problem. I also thought it ill advised to try a landing at ZZZ not knowing my flap condition. We advised ATC we were going around and they gave us an immediate left turn out of the pattern and a climb to 3000'. In the go around; I called for flaps 5 and held out speed at 180 kts. The First Officer moved the flap control lever to 5; but the flaps remained fixed at 16/12. We did retract the gear and I called for the First Officer to get out the QRH and perform the flap asymmetry emergency procedure. I flew and talked with ATC; while the First Officer talked with the flight attendants/passengers; and completed the QRH procedures. A minute or so after our departure from the pattern; ATC asked us to climb to 4000'. I started to climb; but felt the aircraft rolling right and the flaps retracted to 5 without us moving the lever. I stopped the climb and decided we needed to get on the ground ASAP. I told ATC we were unable to climb; I was declaring an emergency and that I wanted vectors to ZZZ1 and their longest runway. Then without warning; the gear horn sounded. With flaps at 5 and the gear up; we decided to lower the gear to get rid of the horn and proceeded with flaps 5; gear down and being vectored to ZZZ1. We landed with a ref speed of 162 kts with auto brakes set to max and max reversing on touchdown. I let the aircraft roll to the end of the runway before I exited; brought the aircraft to a stop; shut down the engines and asked CFR to inspect the wheels; tires; brakes and gear for heat and damage. After about 5 minutes; CFR indicated they found no damage and fairly normal heat for our situation and suggested we could slowly taxi to the gate. To aid CFR in their inspection; I ordered the flaps to be retracted and they did come up when commanded.